The present invention relates generally to precision film resistors, particularly precision film-type power resistors.
A variety of applications require the development of highly precise resistances, which do not vary beyond prescribed tolerances over an acceptable temperature range. One resistor configuration which has found widespread use in this regard is the foil-type resistor, which generally comprises a resistive foil applied to an appropriate substrate. This is because such resistors have been found to be capable of achieving a low temperature coefficient of resistance (TCR). This is generally accomplished by making use of a foil resistive element wherein the foil's resistivity changes with temperature are capable of compensating for the strain induced resistance changes which are developed as a result of mismatch of the coefficients of thermal expansion of the resistive foil and of the substrate to which it is applied, as follows.
Strain (.epsilon.) is capable of being expressed as a function of temperature and as a function of resistance, in accordance with the following equations: EQU .epsilon.=(.alpha.s-.alpha.f).DELTA.T (differential thermal expansion) (A) EQU .epsilon.=1/K .multidot..sup..DELTA.R /R (strain gauge effect) (B)
wherein:
.alpha.s =coefficient of thermal expansion of the substrate material PA1 .alpha.f=coefficient of thermal expansion of the foil material PA1 K =a constant dependent upon the foil material.
Accordingly, in defining changes in resistance as a function of temperature: EQU .sup..DELTA.R /R =K(.alpha.s-.alpha.f).DELTA.T. (C)
With reference to FIG. 1 of the drawings, it will be noted that by appropriate selection of the materials used, the characteristic defined in accordance with equation (C) is capable of being compensated by the foil's resistivity change with temperature .rho.(T)(D). As illustrated in FIG. 2 at (E), such compensation is operational over a range of temperatures. However, such compensation is not perfect because .rho.(T) is non-linear while K(.alpha.s-.alpha.f).DELTA.T is essentially linear. Nevertheless, the resulting temperature coefficient of resistance is very low and very useful for precision applications.
Accordingly, as recognized in U.S. Pat. Nos. 3,405,381 and 3,517,436, issued in the name of Zandman et al, appropriate selection of the materials comprising the substrate and the resistive foil will enable a desired temperature coefficient of resistance to be developed over a certain temperature range. Further in accordance with the teachings of Zandman et al, additional improvement in precision is achieved by compensating the coating which is traditionally used to cover the foil applied to the substrate and the cement which attaches the foil to the substrate with a coating located on the opposite side of the substrate. Attempts to further improve upon the teachings of Zandman et al may be found with reference to U.S. Pat. No. 3,824,521, which teaches adjustment of the coefficients of thermal expansion, and U.S. Pat. No. 4,306,217, which teaches application of a rubber bead to portions of the substrate to absorb forces developed upon its expansion.
While the foregoing efforts have achieved satisfactory results in connection with relatively low power applications, satisfactory results have generally not been achieved when foil resistors of the type previously described were used in relatively high power applications. The reason for this is that unlike low power applications, the current which is applied to the resistive element in a high power application will, upon initiation, cause heating of the resistive foil without significantly heating the substrate to which the foil is attached. This results from differences in the materials used, as well as the thermal barrier which is generally created by the cement which is used to attach the resistive foil to the substrate.
As a result, upon initial application of current, e.g., within a few miliseconds, the foil becomes hot as a result of the current applied to it, while the substrate to which the foil is cemented remains approximately at the temperature it was assuming before the application of current. This is because of the thermal barrier formed by the cement. Even after the heat from the foil passes the cement layer, it will still take some time until all of the substrate becomes hot. During the period of transition between the initial application of current and the time when the entire substrate is at a steady state heat flow (temperature not changing with time), the temperature coefficient of resistance of the resistor will vary. At the time of current initiation, the foil will expand according to its coefficient of thermal expansion (e.g., .alpha.f=9.times.10.sup.-6 /.degree.F.), while the substrate will not expand because it has not yet sensed the change in temperature. Hence, its expansion (.alpha.s) will be zero. In such case, equation (C) will be written as: EQU .sup..DELTA.R /R=K(0-.alpha.f).DELTA.T (C')
Accordingly, there will be an overcompensation of the foil's resistivity .rho.(T) (curve D in FIG. 1), and the resulting temperature coefficient of resistance will be completely different from that shown in FIG. 2. In such case, the temperature coefficient of resistance will be as shown at F in FIG. 3. As time passes, the substrate will become hotter due to heat flow from the foil, and the temperature coefficient of resistance will get closer to its steady state value. Finally, when the substrate is at a steady state temperature, the temperature coefficient of resistance illustrated in FIG. 2 is achieved.
In connection with relatively low speed applications, such considerations presented little difficulty since there was ample time for the components of the resistor to approach temperature equilibrium. However, recent advances in technology have created a need for a precise power resistor which is capable of functioning in relatively high speed operations, and which is capable of establishing precision in the shortest possible period of time. Among various other applications, these include, for example, the application of laser technologies to the etching of integrated circuits as an alternative to the use of photographic masks and the like, the use of lasers for extra fast trimming of resistors, or the use of electron beams for pattern generation.
To illustrate the problem, reference is made to FIG. 4 of the drawings. My studies have found that in connection with a typical power application, resistance will typically vary (.sup..DELTA.R /R) as a function of time as shown at (G). Accordingly, during initial periods of operation, variations in resistance will be such as to preclude useful operation of the device. Only after this initial period passes will acceptable precision be established. For high speed operations, as well as low speed operations, an ideal resistance versus time characteristic such as is illustrated at (H) is desirable.
It has therefore remained to develop a precision power resistor which exhibits a temperature coefficient of resistance which is virtually independent of time and power.